1/2x+2/3x=30

Solution for 1/2x+2/3x=30 equation:

1/2x+2/3x=30

We move all terms to the left:

1/2x+2/3x-(30)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


3x/6x^2+4x/6x^2-30=0

We multiply all the terms by the denominator


3x+4x-30*6x^2=0

We add all the numbers together, and all the variables

7x-30*6x^2=0

Wy multiply elements

-180x^2+7x=0

a = -180; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-180)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-180}=\frac{-14}{-360}
=7/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-180}=\frac{0}{-360}
=0
$